|Jun20-12, 11:38 AM||#1|
Is Thiemann in that group of Madrid skydivers?
Does anybody know?
It takes courage to let go of strict Dirac constraint quantization because maybe your chute will not open. But look at these recent papers from Thomas Thiemann and other members of the Erlangen group! Something is happening there:
Scalar Material Reference Systems and Loop Quantum Gravity
Kristina Giesel, Thomas Thiemann
(Submitted on 17 Jun 2012)
In the past, the possibility to employ (scalar) material reference systems in order to describe classical and quantum gravity directly in terms of gauge invariant (Dirac) observables has been emphasised frequently. This idea has been picked up more recently in Loop Quantum Gravity (LQG) with the aim to perform a reduced phase space quantisation of the theory thus possibly avoiding problems with the (Dirac) operator constraint quantisation method for constrained system. In this work, we review the models that have been studied on the classical and/or the quantum level and parametrise the space of theories so far considered. We then describe the quantum theory of a model that, to the best of our knowledge, so far has only been considered classically. This model could arguably called the optimal one in this class of models considered as it displays the simplest possible true Hamiltonian while at the same time reducing all constraints of General Relativity.
Loop quantum gravity without the Hamiltonian constraint
Norbert Bodendorfer, Alexander Stottmeister, Andreas Thurn
(Submitted on 29 Mar 2012)
We show that under certain technical assumptions, including a generalisation of CMC foliability and strict positivity of the scalar field, general relativity conformally coupled to a scalar field can be quantised on a partially reduced phase space, meaning reduced only with respect to the Hamiltonian constraint and a proper gauge fixing. More precisely, we introduce, in close analogy to shape dynamics, the generator of a local conformal transformation acting on both, the metric and the scalar field. A new metric, which is invariant under this transformation, is constructed and used to define connection variables which can be quantised by standard loop quantum gravity methods. Since this connection is invariant under the local conformal transformation, the generator of which is shown to be a good gauge fixing for the Hamiltonian constraint, the Dirac bracket associated with implementing these constraints coincides with the Poisson bracket for the connection. Thus, the well developed kinematical quantisation techniques for loop quantum gravity are available, while the Hamiltonian constraint has been solved (more precisely, gauge fixed) classically. The physical interpretation of this system is that of general relativity on a fixed spatial slice, the associated "time" of which is given by the value of the generator of local conformal transformations. While it is hard to address dynamical problems in this framework (due to the complicated "time" function), it seems, due to good accessibility properties of the gauge in certain situations, to be well suited for problems such as the computation of black hole entropy, where actual physical states can be counted and the dynamics is only of indirect importance. Also, the interpretation of the geometric operators gets an interesting twist, which exemplifies the deep relationship between observables and the choice of a time function.
Linking Covariant and Canonical General Relativity via Local Observers
Steffen Gielen, Derek K. Wise
(Submitted on 4 Jun 2012)
Hamiltonian gravity, relying on arbitrary choices of "space," can obscure spacetime symmetries. We present an alternative, manifestly spacetime covariant formulation that nonetheless distinguishes between "spatial" and "temporal" variables. The key is viewing dynamical fields from the perspective of a field of observers -- a unit timelike vector field that also transforms under local Lorentz transformations. On one hand, all fields are spacetime fields, covariant under spacetime symmeties. On the other, when the observer field is normal to a spatial foliation, the fields automatically fall into Hamiltonian form, recovering the Ashtekar formulation. We argue this provides a bridge between Ashtekar variables and covariant phase space methods. We also outline a framework where the 'space of observers' is fundamental, and spacetime geometry itself may be observer-dependent.
8 pages; Essay written for the 2012 Gravity Research Foundation Awards for Essays on Gravitation
Notice that Kristina is a Prof at Erlangen, Derek Wise (a Baez PhD) is postdoc there, and Bodendorfer Stottmeister and Thurn are Thiemann's grad students. If there is a move, it is concerted. The Gielen Wise approach has a special interest to me because "field of observers" takes the place of dust, ancient light, CMB, etc---and there can be a space of such "observer fields."
So I am wondering, was Thiemann part of that famous group of Madrid skydivers? I can't recognize several of the people in the airplane. Francesca of course I recognize! And Johannes Tambornino is the guy with the red jacket. Simone Speziale is the guy diving with Rovelli. But I have the feeling that Thomas is also there! I just can't be sure.
Does anybody know?
|Jun20-12, 12:12 PM||#2|
In fact that is exactly what one does in cosmology. One takes the field of observers who are at rest with respect to the Cosmic Microwave Background (each one in his separate galaxy or out somewhere in between galaxies) and defines many things precisely on the basis of that field. (proper distance, universal time, the terms in Hubble equation's pattern of expansion)
Before cosmologists knew about the CMB they defined the same field of observers to be those at rest relative to the expansion process itself (the "Hubble flow"). These were the ISOTROPIC observers, for whom the Hubble law expansion appeared the same in all directions. A lot of cosmology was built on that conceptual basis.
Now it is easier to talk about because the isotropic observers are simply those for whom there is no Doppler hotspot in the microwave sky. They are not moving with respect to the ancient light. So the temperature is approximately the same in all directions for them.
Obviously this is not a single observer reference frame, it is a FIELD of stationary observers. So I think it was a good idea of Gielen Wise to take this simple basic idea from cosmology into quantum gravity. And I don't see a lot of difference between that field of observers and the MATERIAL reference system of Thiemann Giesel.
|Jun21-12, 06:26 AM||#3|
I prefer the beach...
|Jun21-12, 09:48 PM||#4|
Is Thiemann in that group of Madrid skydivers?
But I also have to say that skydiving looks like a lot of fun.
Be that as it may, there is what looks to me like a new departure at Erlangen. It looks to me like a concerted move in the direction of formulations which could involve a Hamiltonian but which are not strictly Dirac. A sense of jumping free of constraints. I could be wrong, and I'd like to hear how other people see the Erlangen group's new papers.
|Jun24-12, 08:36 AM||#6|
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